Focal shifts of focused partially coherent electromagnetic beams

Based on the effective Fresnel number, a simple analytical expression is presented to evaluate the relative focal shift in a circular-aperture lens system which is illuminated by a partially coherent electromagnetic beam. The effective Fresnel number is dependent not only on real Fresnel number but also on the polarization distribution and spatial coherent lengths of two polarized components of the incident partially coherent electromagnetic beam. It is shown that the relative focal shift is just determined by the effective Fresnel number. The results indicate that this new method can evaluate the focal shifts simply and exactly.